Problem: You are given three integers a, b, k.

Find two binary integers x and y (x ≥ y) such that 

  1. both x and y consist of a zeroes and b ones; 
  2. x - y (also written in binary form) has exactly k ones. 

You are not allowed to use leading zeros for x and y. 

Input

The only line contains three integers a, b, and k (0 ≤ a; 1 ≤ b; 0 ≤ k ≤ a + b ≤ 2 ⋅ 10^5) — the number of zeroes, ones, and the number of ones in the result.

Output

If it's possible to find two suitable integers, print "Yes" followed by x and y in base-2.

Otherwise print "No".

If there are multiple possible answers, print any of them.

Examples

Input


4 2 3


Output


Yes
101000
100001


Input


3 2 1


Output


Yes
10100
10010


Input


3 2 5


Output


No

Note

In the first example, x = 101000_2 = 2^5 + 2^3 = 40_{10}, y = 100001_2 = 2^5 + 2^0 = 33_{10}, 40_{10} - 33_{10} = 7_{10} = 2^2 + 2^1 + 2^0 = 111_{2}. Hence x-y has 3 ones in base-2.

In the second example, x = 10100_2 = 2^4 + 2^2 = 20_{10}, y = 10010_2 = 2^4 + 2^1 = 18, x - y = 20 - 18 = 2_{10} = 10_{2}. This is precisely one 1.

In the third example, one may show, that it's impossible to find an answer.

Solution (in PYTHON3):

Solution:
'''Author- Akshit Monga'''
from sys import stdin, stdout
# input = stdin.readline
t = 1
for _ in range(t):
    a,b,k=map(int,input().split())
    if a==0 and k==0:
        print("YES")
        val=['1' for i in range(b)]
        s="".join(val)
        print(s)
        print(s)
        continue
    if a==0:
        print("NO")
        continue
    if k>(a+b-2):
        print("NO")
        continue
    if b==1:
        if k!=0:
            print("NO")
            continue
        print("YES")
        out=['1']
        for i in range(a):
            out.append('0')
        s=''.join(out)
        print(s)
        print(s)
        continue
    if k==0:
        print("YES")
        val=[]
        for i in range(b):
            val.append('1')
        for i in range(a):
            val.append('0')
        s=''.join(val)
        print(s)
        print(s)
        continue
    val1=[]
    val2=[]
    if k<=a:
        val1 = []
        val2 = []
        for i in range(b):
            val1.append('1')
            if i == b - 1:
                val2.append('0')
            else:
                val2.append('1')
        count = 0
        for i in range(a):
            val1.append('0')
            count += 1
            if count == k:
                val2.append('1')
            else:
                val2.append('0')
        s1 = ''.join(val1)
        s2 = ''.join(val2)
        print("YES")
        print(s1)
        print(s2)
        continue
    for i in range(b):
        val1.append('1')
    for i in range(a):
        val1.append('0')
    val2.append('1')
    c=0
    for i in range(a-1):
        val2.append('0')
    k-=a
    used=1
    for i in range(k):
        used+=1
        val2.append('1')
    val2.append('0')
    for i in range(b-used):
        val2.append('1')
    val2=val2[::-1]
    s1=''.join(val1)
    s2=''.join(val2)
    print("YES")
    print(s1)
    print(s2)